Based on first-principles total-energy calculation, we investigate the electronic structures of bilayer graphene, one of which layers possesses atomic or topological defects, to explore the possibility of band gap engineering of graphene by means of physisorption of defective graphene. Our calculations show that the pristine graphene layer possesses a finite energy gap between bonding and antibonding π states because of the potential undulation caused by the other graphene layers with defects. We also found that the gap values strongly depend on the defect species and their mutual arrangement with respect to the pristine layer.